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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Two examples of Borel partially ordered sets with the countable chain condition


Author: Stevo Todorčević
Journal: Proc. Amer. Math. Soc. 112 (1991), 1125-1128
MSC: Primary 03E05; Secondary 03E15, 54H05
DOI: https://doi.org/10.1090/S0002-9939-1991-1069693-7
MathSciNet review: 1069693
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Abstract: We define an open symmetric two-place relation on the reals such that the reals cannot be covered by countably many sets of related elements, but there is no uncountable set of unrelated elements. The poset $ \mathcal{P}$ of finite sets of related elements satisfies the countable chain condition but it may fail to have the property K, i.e., a substantial irregularity can be injected in $ \mathcal{P}$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1069693-7
Article copyright: © Copyright 1991 American Mathematical Society

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